Create , Visualize & Explore

Sangeeta Gulati, vidishatangri.29, Nov 28, 2015

This workbook has collection of worksheets which will be (re)created and explored during the workshop "Create , Visualize & explore with GeoGebra and Desmos" for secondary and senior secondary mathematics teachers on November 27 & 28, 2015. This workshop will be held at Sanskriit School , New Delhi, India and will be led by Sangeeta Gulati.

Table of Contents

  1. Geometry
    1. Drawings, Constructions, and Drag Test
    2. Construction vs Drawing
    3. Pythagoras Theorem for Regular n-gons
    4. Disection Proof - Pythagoras Theorem
    5. Corners of Squares
    6. Pentagrams
    7. Angle Sum Property by Rotation
    8. Isosceles Triangles - Examples and Non-Examples
    9. Midpoint Triangles
    10. Intro to Area Using Unit Squares
    11. Dividing a line segment into 4 equal parts
    12. Exterior Angles of a Regular Polygon
    13. Consistency of Linear equations in Two Variables
    14. Perimeter - Area Challenges
  2. PreCalculus
    1. Function Matching
    2. Investigating Trigonometry
    3. Investigating Trigonometry 2
    4. Radians, Number line and the Unit Circle
    5. Sine Curve with Points
    6. Domain of Functions
    7. Horizontal Line Test
    8. Trigonometric Functions and Unit Circle
    9. Inverse of a Function-Reflection on y = x
    10. Vertical Line Test
    11. Histogram with GeoGebra
  3. Calculus
    1. Understanding Differentiability
    2. Derivative as Slope Function
    3. Increasing and Decreasing Functions-Intervals
    4. Definite Integral - Upper and Lower Sum
    5. GeoGebra Calculus Applets
  4. Linear Programming
    1. Linear Programming- Problem 2- Minimum Cost
    2. Linear Programming-Transport Problem
  5. Vectors & Three Dimensional Geometry
    1. Definition of vector addition
    2. Translations along vector
    3. Vector Sum - Parallelogram Law
    4. Skew Lines and Line of Shortest Distance
    5. Three Dimensional Coordinate System with Axes Planes
    6. Point in 3D Coordinate System
  6. Conics
    1. Parabola
    2. Ellipse
  7. Maths is Beautiful
    1. 8 Point Star
    2. Square Root Spiral
    3. Golden Spiral
    4. Caso 5
    5. Sierpinski Triangle
    6. Ever Present Equilateral Triangle
    7. Curve of Pursuit
    8. Snowflakes with GeoGebra
    9. Kaleidoscope
  8. GeoGebra Guides

1.

Geometry

Worksheets suitable for middle and secondary school mathematics.

  • 1. Drawings, Constructions, and Drag Test
  • 2. Construction vs Drawing
  • 3. Pythagoras Theorem for Regular n-gons
  • 4. Disection Proof - Pythagoras Theorem
  • 5. Corners of Squares
  • 6. Pentagrams
  • 7. Angle Sum Property by Rotation
  • 8. Isosceles Triangles - Examples and Non-Examples
  • 9. Midpoint Triangles
  • 10. Intro to Area Using Unit Squares
  • 11. Dividing a line segment into 4 equal parts
  • 12. Exterior Angles of a Regular Polygon
  • 13. Consistency of Linear equations in Two Variables
  • 14. Perimeter - Area Challenges

1.1.

Drawings, Constructions, and Drag Test

Discussion
[b][font=Tahoma, sans-serif][color=#000000]What is the difference between a drawing and a construction?[/color][/font][/b][br][font=Tahoma, sans-serif][color=#000000] Adrawing is only a connection of points and lines that can be shaped[br]in the form of a geometric figure, while a construction is a solid[br]object with constraints and properties.[/color][color=#000000][br][br][b]What is the “drag test” and why is it important?[/b][/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]To see if the construction is fully defined. [/color][color=#000000]Tocheck if the construction is correct.[/color][color=#000000][br][br][b]Why is it important to construct figures instead of just drawing them[br]in interactive geometry software?[/b][/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]To be able to work with them, so the construction can influence other[br]objects and vice versa.[/color][color=#000000][br][br][b]What do we have to know about the geometric figure before we are able[/b][br]to construct it using dynamic mathematics software?[/color][/font][br][font=Tahoma, sans-serif][color=#000000] [/color][color=#000000]Dimensions,number of vertices. [/color][color=#000000][br][/color][/font][br][br]
– Jose Alvarado

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

1.14.

–

2.

PreCalculus

[color=#1551b5]Worksheets to teach and explore Trigonometry , Trigonometric functions, Domain and Range of functions, Graphs of Functions[/color]

  • 1. Function Matching
  • 2. Investigating Trigonometry
  • 3. Investigating Trigonometry 2
  • 4. Radians, Number line and the Unit Circle
  • 5. Sine Curve with Points
  • 6. Domain of Functions
  • 7. Horizontal Line Test
  • 8. Trigonometric Functions and Unit Circle
  • 9. Inverse of a Function-Reflection on y = x
  • 10. Vertical Line Test
  • 11. Histogram with GeoGebra

2.1.

Function Matching

This activity is a matching test. Drag the correct function to its graph.[br][br]Displayed in English as Daniel Mentrard gave permission.[br][url]http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/MDfonctioalg.html[/url]
By Daniel Mentrard, Créé avec GeoGebra [url]http://dmentrard.free.fr/GEOGEBRA/index.htm[\url][br]Translation by A. B. Cron
– Auston B Cron

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

2.10.

–

2.11.

–

3.

Calculus

Abstract concepts of Calculus are best illustrated with dynamic applets made by GeoGebra

  • 1. Understanding Differentiability
  • 2. Derivative as Slope Function
  • 3. Increasing and Decreasing Functions-Intervals
  • 4. Definite Integral - Upper and Lower Sum
  • 5. GeoGebra Calculus Applets

3.1.

Understanding Differentiability

Drag the point B (x, f(x)) to see how a Secant Becomes a Tangent Use the check boxes to see the slopes of the Secant line and of the Tangent line

This applte shows how a Secant Becomes a Tangent and it shows the slopes of the Secant line and of the Tangent line , thus establishing a correspondence between differentiability geometrically and algebraically.
– Sangeeta Gulati

3.2.

–

3.3.

–

3.4.

–

3.5.

–

4.

Linear Programming

These applets are based on the Linear Programming problems of class XII text book.

  • 1. Linear Programming- Problem 2- Minimum Cost
  • 2. Linear Programming-Transport Problem

4.1.

Linear Programming- Problem 2- Minimum Cost

Minimum Cost- Verification
– Sangeeta Gulati

4.2.

–

5.

Vectors & Three Dimensional Geometry

  • 1. Definition of vector addition
  • 2. Translations along vector
  • 3. Vector Sum - Parallelogram Law
  • 4. Skew Lines and Line of Shortest Distance
  • 5. Three Dimensional Coordinate System with Axes Planes
  • 6. Point in 3D Coordinate System

5.1.

Definition of vector addition

Dynamic demonstration of vector addition.
– Malin Christersson

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

6.

Conics

  • 1. Parabola
  • 2. Ellipse

6.1.

Parabola

Parabola formed as envelope of straight lines.
Parabola
– Sangeeta Gulati

6.2.

–

7.

Maths is Beautiful

[color=#1551b5]There are many math wonders that one can discover and recreate with the help of technology , especially GeoGebra. Here is a collection of some of them.[/color]

  • 1. 8 Point Star
  • 2. Square Root Spiral
  • 3. Golden Spiral
  • 4. Caso 5
  • 5. Sierpinski Triangle
  • 6. Ever Present Equilateral Triangle
  • 7. Curve of Pursuit
  • 8. Snowflakes with GeoGebra
  • 9. Kaleidoscope

7.1.

8 Point Star

Maths is fun!
8 Point Star
– Sangeeta Gulati

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

7.9.

–

8.

GeoGebra Guides

[color=#c51414]Collection of GeoGebra help guides with tutorials to help you learn GeoGebra[/color] [url]http://tube.geogebra.org/material/simple/id/1403161[/url]


    This chapter does not contain any resources yet.

Information